Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	13703
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	963.6 KiB
Average record size in memory	72.0 B

Variable types

NUM	9

Warnings

`mean_closeness` is highly correlated with `average_clustering` and 1 other fields	High correlation
`average_clustering` is highly correlated with `mean_closeness` and 1 other fields	High correlation
`assortativity` is highly correlated with `average_clustering` and 1 other fields	High correlation
`rg` has unique values	Unique
`shape` has unique values	Unique

Reproduction

Analysis started	2020-11-27 01:59:08.132770
Analysis finished	2020-11-27 01:59:22.628910
Duration	14.5 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

rg
Real number (ℝ_≥0)

UNIQUE

Distinct	13703
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.4053879859
Minimum	0.2647429215
Maximum	0.553959391
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	0.2647429215
5-th percentile	0.316142869
Q1	0.3761514338
median	0.4080868467
Q3	0.4348126528
95-th percentile	0.4804880947
Maximum	0.553959391
Range	0.2892164694
Interquartile range (IQR)	0.058661219

Descriptive statistics

Standard deviation	0.04856659662
Coefficient of variation (CV)	0.1198027527
Kurtosis	0.08702454773
Mean	0.4053879859
Median Absolute Deviation (MAD)	0.03060915531
Skewness	-0.02886839327
Sum	5555.031571
Variance	0.002358714307
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.4166188819	1	< 0.1%
0.319555027	1	< 0.1%
0.4279362097	1	< 0.1%
0.3775160056	1	< 0.1%
0.4236557521	1	< 0.1%
0.3934568128	1	< 0.1%
0.3856058298	1	< 0.1%
0.3720310206	1	< 0.1%
0.4016123154	1	< 0.1%
0.3601770074	1	< 0.1%
Other values (13693)	13693	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.2647429215	1	< 0.1%
0.2663038185	1	< 0.1%
0.2668979912	1	< 0.1%
0.2674296361	1	< 0.1%
0.2674408081	1	< 0.1%

Value	Count	Frequency (%)
0.553959391	1	< 0.1%
0.5534800489	1	< 0.1%
0.5528707909	1	< 0.1%
0.5522530673	1	< 0.1%
0.55201942	1	< 0.1%

mean_displacement
Real number (ℝ_≥0)

Distinct	13633
Distinct (%)	99.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	14.36289176
Minimum	0
Maximum	142.2368066
Zeros	71
Zeros (%)	0.5%
Memory size	107.1 KiB

Quantile statistics

Minimum	0
5-th percentile	1.203558696
Q1	6.592146559
median	10.31254505
Q3	20.77357781
95-th percentile	38.04664558
Maximum	142.2368066
Range	142.2368066
Interquartile range (IQR)	14.18143125

Descriptive statistics

Standard deviation	11.68200973
Coefficient of variation (CV)	0.8133466382
Kurtosis	4.302220454
Mean	14.36289176
Median Absolute Deviation (MAD)	4.869084109
Skewness	1.477814807
Sum	196814.7058
Variance	136.4693512
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	71	0.5%
15.79393212	1	< 0.1%
25.30294971	1	< 0.1%
8.859828664	1	< 0.1%
10.91719244	1	< 0.1%
29.30264892	1	< 0.1%
8.425796832	1	< 0.1%
10.16118308	1	< 0.1%
6.399548839	1	< 0.1%
8.641484774	1	< 0.1%
Other values (13623)	13623	99.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	71	0.5%
1.016666045	1	< 0.1%
1.023916176	1	< 0.1%
1.034306103	1	< 0.1%
1.035238929	1	< 0.1%

Value	Count	Frequency (%)
142.2368066	1	< 0.1%
119.4764542	1	< 0.1%
117.6691426	1	< 0.1%
115.4518361	1	< 0.1%
105.9717172	1	< 0.1%

shape
Real number (ℝ)

UNIQUE

Distinct	13703
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.004182291781
Minimum	-0.06826915628
Maximum	0.1877051027
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	-0.06826915628
5-th percentile	-0.00569033166
Q1	-0.001052393195
median	0.0004036715331
Q3	0.003431179983
95-th percentile	0.0319963595
Maximum	0.1877051027
Range	0.2559742589
Interquartile range (IQR)	0.004483573177

Descriptive statistics

Standard deviation	0.01661281353
Coefficient of variation (CV)	3.972179465
Kurtosis	30.47326611
Mean	0.004182291781
Median Absolute Deviation (MAD)	0.002056363178
Skewness	4.472019201
Sum	57.30994428
Variance	0.0002759855735
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
-0.0003409817565	1	< 0.1%
-0.002557742447	1	< 0.1%
-0.001713315084	1	< 0.1%
-0.02713212997	1	< 0.1%
0.009597846401	1	< 0.1%
2.308752524e-05	1	< 0.1%
0.0002158479906	1	< 0.1%
0.009361954138	1	< 0.1%
-0.0002341870525	1	< 0.1%
0.002582613462	1	< 0.1%
Other values (13693)	13693	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
-0.06826915628	1	< 0.1%
-0.06363906968	1	< 0.1%
-0.05977766999	1	< 0.1%
-0.05755228497	1	< 0.1%
-0.05519934157	1	< 0.1%

Value	Count	Frequency (%)
0.1877051027	1	< 0.1%
0.1786923401	1	< 0.1%
0.1755746789	1	< 0.1%
0.1755451367	1	< 0.1%
0.1737699482	1	< 0.1%

density
Real number (ℝ_≥0)

Distinct	9829
Distinct (%)	71.7%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.001444083549
Minimum	0.001331047295
Maximum	0.001676962743
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	0.001331047295
5-th percentile	0.001361556332
Q1	0.001403173627
median	0.001445711122
Q3	0.001482920248
95-th percentile	0.001533014509
Maximum	0.001676962743
Range	0.0003459154478
Interquartile range (IQR)	7.974662057e-05

Descriptive statistics

Standard deviation	5.35448747e-05
Coefficient of variation (CV)	0.03707879279
Kurtosis	-0.5430892429
Mean	0.001444083549
Median Absolute Deviation (MAD)	3.944956711e-05
Skewness	0.1890523753
Sum	19.78827688
Variance	2.867053606e-09
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.001359397863	9	0.1%
0.001386100755	8	0.1%
0.001377112707	8	0.1%
0.001416759773	7	0.1%
0.001375511413	7	0.1%
0.001365518738	7	0.1%
0.001359883659	7	0.1%
0.001371642042	7	0.1%
0.001427524456	6	< 0.1%
0.001385919823	6	< 0.1%
Other values (9819)	13631	99.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.001331047295	1	< 0.1%
0.001331475832	1	< 0.1%
0.001333950507	1	< 0.1%
0.001334217447	1	< 0.1%
0.001334590359	1	< 0.1%

Value	Count	Frequency (%)
0.001676962743	1	< 0.1%
0.001633652961	1	< 0.1%
0.001629685157	1	< 0.1%
0.001628587822	1	< 0.1%
0.001627807059	1	< 0.1%

clique_number
Real number (ℝ_≥0)

Distinct	7
Distinct (%)	0.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	4.13084726
Minimum	2
Maximum	8
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	2
5-th percentile	3
Q1	3
median	4
Q3	4
95-th percentile	7
Maximum	8
Range	6
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	1.141959601
Coefficient of variation (CV)	0.2764468231
Kurtosis	0.6922155377
Mean	4.13084726
Median Absolute Deviation (MAD)	1
Skewness	1.135683239
Sum	56605
Variance	1.304071731
Monotocity	Not monotonic

Histogram with fixed size bins (bins=7)

Value	Count	Frequency (%)
4	6254	45.6%
3	4239	30.9%
6	1300	9.5%
5	1095	8.0%
7	725	5.3%
8	57	0.4%
2	33	0.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
2	33	0.2%
3	4239	30.9%
4	6254	45.6%
5	1095	8.0%
6	1300	9.5%

Value	Count	Frequency (%)
8	57	0.4%
7	725	5.3%
6	1300	9.5%
5	1095	8.0%
4	6254	45.6%

average_clustering
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	12627
Distinct (%)	92.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.153942953
Minimum	0
Maximum	0.6084742648
Zeros	33
Zeros (%)	0.2%
Memory size	107.1 KiB

Quantile statistics

Minimum	0
5-th percentile	0.008762151113
Q1	0.0417315056
median	0.06461505922
Q3	0.1513957745
95-th percentile	0.6000244783
Maximum	0.6084742648
Range	0.6084742648
Interquartile range (IQR)	0.1096642689

Descriptive statistics

Standard deviation	0.190103778
Coefficient of variation (CV)	1.234897566
Kurtosis	1.32432533
Mean	0.153942953
Median Absolute Deviation (MAD)	0.05288079484
Skewness	1.693284119
Sum	2109.480285
Variance	0.03613944639
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	33	0.2%
0.04424778761	10	0.1%
0.04879074658	10	0.1%
0.04620253165	9	0.1%
0.0443318556	9	0.1%
0.04427577483	8	0.1%
0.04885238998	7	0.1%
0.0443599493	7	0.1%
0.0483396385	7	0.1%
0.04430379747	7	0.1%
Other values (12617)	13596	99.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	33	0.2%
0.001049538203	1	< 0.1%
0.001050199538	1	< 0.1%
0.001056859015	1	< 0.1%
0.001058873359	1	< 0.1%

Value	Count	Frequency (%)
0.6084742648	1	< 0.1%
0.6081231788	1	< 0.1%
0.6079907524	1	< 0.1%
0.6075260817	1	< 0.1%
0.6074839567	1	< 0.1%

mean_closeness
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	13699
Distinct (%)	> 99.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.0005908148564
Minimum	6.518191387e-05
Maximum	0.003373289354
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	6.518191387e-05
5-th percentile	0.0001134520943
Q1	0.00016472718
median	0.0003500128228
Q3	0.00062236653
95-th percentile	0.002000550186
Maximum	0.003373289354
Range	0.00330810744
Interquartile range (IQR)	0.0004576393501

Descriptive statistics

Standard deviation	0.0006084340776
Coefficient of variation (CV)	1.029821899
Kurtosis	1.650645658
Mean	0.0005908148564
Median Absolute Deviation (MAD)	0.0002214302598
Skewness	1.649788789
Sum	8.095935978
Variance	3.701920268e-07
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
8.821303762e-05	2	< 0.1%
0.0001025763384	2	< 0.1%
0.0001064349032	2	< 0.1%
0.0001050572457	2	< 0.1%
0.00188611883	1	< 0.1%
0.0005321168535	1	< 0.1%
0.0005422710336	1	< 0.1%
0.002055568074	1	< 0.1%
0.0001030821339	1	< 0.1%
0.0005829913736	1	< 0.1%
Other values (13689)	13689	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
6.518191387e-05	1	< 0.1%
6.662907439e-05	1	< 0.1%
6.705958217e-05	1	< 0.1%
6.865560023e-05	1	< 0.1%
6.974804513e-05	1	< 0.1%

Value	Count	Frequency (%)
0.003373289354	1	< 0.1%
0.003258571217	1	< 0.1%
0.003248603873	1	< 0.1%
0.003212554094	1	< 0.1%
0.00317817879	1	< 0.1%

mean_betweenness
Real number (ℝ_≥0)

Distinct	11988
Distinct (%)	87.5%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	4.35480376e-05
Minimum	0
Maximum	0.00367050182
Zeros	1
Zeros (%)	< 0.1%
Memory size	107.1 KiB

Quantile statistics

Minimum	0
5-th percentile	1.326133315e-08
Q1	3.875270523e-08
median	3.456921373e-07
Q3	7.214904809e-07
95-th percentile	0.0002834931719
Maximum	0.00367050182
Range	0.00367050182
Interquartile range (IQR)	6.827377757e-07

Descriptive statistics

Standard deviation	0.0001569834597
Coefficient of variation (CV)	3.604834302
Kurtosis	129.7701919
Mean	4.35480376e-05
Median Absolute Deviation (MAD)	3.120396498e-07
Skewness	9.121425338
Sum	0.5967387593
Variance	2.464380663e-08
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1.366464407e-08	10	0.1%
2.621746929e-08	8	0.1%
1.518293785e-08	7	0.1%
1.521178447e-08	7	0.1%
8.036414925e-09	7	0.1%
1.014118965e-08	7	0.1%
2.05458807e-08	6	< 0.1%
1.313360891e-08	6	< 0.1%
1.946777186e-08	6	< 0.1%
3.09894319e-08	6	< 0.1%
Other values (11978)	13633	99.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	< 0.1%
5.003793606e-10	1	< 0.1%
5.013264509e-10	2	< 0.1%
5.109301499e-10	1	< 0.1%
1.004551866e-09	1	< 0.1%

Value	Count	Frequency (%)
0.00367050182	1	< 0.1%
0.003219041872	1	< 0.1%
0.003209295734	1	< 0.1%
0.002818780816	1	< 0.1%
0.002789564268	1	< 0.1%

assortativity
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	13701
Distinct (%)	> 99.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.8308015712
Minimum	0.4461152309
Maximum	1
Zeros	0
Zeros (%)	0.0%
Memory size	107.1 KiB

Quantile statistics

Minimum	0.4461152309
5-th percentile	0.5068282155
Q1	0.8078689932
median	0.8636668274
Q3	0.9396527637
95-th percentile	0.9716369327
Maximum	1
Range	0.5538847691
Interquartile range (IQR)	0.1317837705

Descriptive statistics

Standard deviation	0.1441273849
Coefficient of variation (CV)	0.1734799137
Kurtosis	0.6438379083
Mean	0.8308015712
Median Absolute Deviation (MAD)	0.06513195912
Skewness	-1.323601398
Sum	11384.47393
Variance	0.02077270307
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.9785965306	2	< 0.1%
0.9872670689	2	< 0.1%
0.7951487579	1	< 0.1%
0.7860096934	1	< 0.1%
0.8588633348	1	< 0.1%
0.8876308903	1	< 0.1%
0.8145419118	1	< 0.1%
0.8012380293	1	< 0.1%
0.9271406418	1	< 0.1%
0.9448878065	1	< 0.1%
Other values (13691)	13691	99.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.4461152309	1	< 0.1%
0.4540455353	1	< 0.1%
0.4553403686	1	< 0.1%
0.4558974838	1	< 0.1%
0.4588284583	1	< 0.1%

Value	Count	Frequency (%)
1	1	< 0.1%
0.9951357386	1	< 0.1%
0.994873844	1	< 0.1%
0.9936089067	1	< 0.1%
0.9930572686	1	< 0.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	rg	mean_displacement	shape	density	clique_number	average_clustering	mean_closeness	mean_betweenness	assortativity
0	0.474618	0.000000	0.000306	0.001343	3	0.005668	0.000083	5.003794e-10	0.994874
1	0.464732	20.724373	-0.000009	0.001347	2	0.000000	0.000082	5.080235e-09	0.961830
2	0.461643	20.079818	0.000013	0.001350	2	0.000000	0.000092	8.036415e-09	0.938803
3	0.458490	22.115586	0.000187	0.001349	2	0.000000	0.000088	3.019367e-09	0.967801
4	0.456447	21.998844	0.000182	0.001351	3	0.004840	0.000090	4.537639e-09	0.964951
5	0.452112	22.708864	0.000328	0.001366	3	0.007581	0.000106	1.818500e-08	0.962455
6	0.450899	15.669330	0.000252	0.001349	3	0.003371	0.000087	9.615861e-09	0.963636
7	0.444741	24.677752	0.000165	0.001370	3	0.001473	0.000110	1.008364e-08	0.941677
8	0.437936	25.683807	-0.000002	0.001367	3	0.005271	0.000104	5.577654e-09	0.952807
9	0.436538	19.690475	0.000124	0.001383	4	0.006293	0.000128	1.098756e-08	0.952529

Last rows

	rg	mean_displacement	shape	density	clique_number	average_clustering	mean_closeness	mean_betweenness	assortativity
13693	0.419452	1.066486	-0.001544	0.001425	6	0.603132	0.001725	0.000158	0.508937
13694	0.419593	1.058365	-0.001591	0.001427	7	0.601294	0.001761	0.000164	0.512684
13695	0.419346	1.048077	-0.001521	0.001423	6	0.601037	0.001724	0.000158	0.505704
13696	0.419695	1.081644	-0.001482	0.001427	6	0.600851	0.001757	0.000181	0.521546
13697	0.419467	1.040956	-0.001504	0.001426	6	0.600861	0.001762	0.000164	0.512302
13698	0.419562	1.111165	-0.001583	0.001423	6	0.601393	0.001656	0.000129	0.497360
13699	0.419378	1.070154	-0.001506	0.001425	6	0.601044	0.001658	0.000130	0.512344
13700	0.419409	1.048686	-0.001516	0.001429	6	0.601688	0.001671	0.000124	0.502967
13701	0.419777	1.034306	-0.001443	0.001425	6	0.599784	0.001668	0.000124	0.501561
13702	0.419195	1.079562	-0.001524	0.001426	6	0.602202	0.001727	0.000158	0.505160

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows